Recent Advances in Econometric Modeling and Forecasting Techniques for Tourism Demand Prediction
Hala Hilaly Tourism Studies Department, Faculty of Tourism and Hotels, Alexandria University
[email protected]
Hisham El-Shishiny Advanced Technology and Center for Advanced Studies, IBM Cairo Technology Development Center
[email protected]
Abstract Along with the development of forecasting techniques, a large number of methods have been applied to the tourism demand prediction area. The focus of this study is on the econometric models. The study provides a full account of different econometric models used in modeling and forecasting tourism demand. Traditional regression approaches suffer from different limitations such as the structure instability, the spurious regression. Furthermore, it ignores recent developments particularly in the areas of diagnostic checking, error correction models and co-integration. The study provides a review of alternative econometric techniques, and demonstrates the advantages/disadvantages of each model. Moreover, this study presents some emerging new modeling and forecasting techniques such as the Tourism Technical Analysis System (TTAS) model and Artificial Intelligence (AI) techniques. Keywords: Econometric models, Tourism Demand, Forecasting
approaches are divided into: Time series models, econometric models, and other recent emerging models. The purpose of this study is to provide a full account on all the econometric models used in tourism demand modeling and prediction as well as some emerging new techniques. The main objective therefore is to review different econometric methods used to forecast tourism demand in various destinations, and to demonstrate the advantages/disadvantages of each model, as well as the limitations of application of each model. The rest of this paper is organized as follows. In section2, the main tourism prediction models are presented including time series models, econometric models, artificial intelligence techniques as well as the tourism technical analysis system. In section3, econometric modeling are illustrated, a discussion provided the main advantages and limitations of different models are provided in section4. The final section concludes the study.
2. Main Tourism Prediction Models 2.1 Time series models
1. Introduction In the last few decades, international tourism demand has thoroughly attracted academic interest resulting in a wide range of successful forecasting approaches. Forecasting tourism demand is not only important for planners and policy makers but also for researchers who are interested in tourism demand modeling approaches to improve forecasting accuracy. Most of the recent studies focus on the application of different techniques, both qualitative and quantitative, to model and forecast the demand for tourism in various destinations. Quantitative forecasting
Time series models or non-causal quantitative models, assume that a variable may be forecast without reference to the factors which determine the level of that variable. Patterns of the data during the past are used to project the future values [54]. It is rarely possible to justify time series models on the basis of theory. The reasons for their use are essentially pragmatic; they often generate acceptable forecasts, therefore they have been widely used for tourism demand forecasting in the past decades. The time series models include: Naïve 1 and 2, exponential smoothing, trend curve analysis, Gompertz, simple autoregressive, and the integrated
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autoregressive moving average (ARIMA) either simple ARIMA or seasonal ARIMA ( SARIMA) models. The later has been used frequently over the last few years as seasonality is a dominant feature in tourism demand. Some recent research extended the univariate timeseries models to a multivariate dimension (MARIMA) such as [11, 15 and 16]. There was a consensus that the multivariate ARIMA performs the simple ARIMA. Another effort has been to extend Univariate time series analysis of tourism demand to the application of the Generalized Autoregressive Conditional Heteroskedastic (GARCH) model [6].
the current interest has been focused on less precise heuristic methods, notably genetic algorithms, fuzzy logic, artificial neural networks and support vector machine(s) [50]. The main advantage of AI techniques that they do not require any preliminary or additional information about data such as distribution or probability [43]. Although, they embody some important limitations. For example, they lack a theoretical underpinning, and are unable to interpret tourism demand from the economic perspective, and therefore provide very little help in policy evaluation [29].
2.2. Econometric models
2.3.1.1 The artificial neural network (ANN) method. The main advantage of this method is the ability to adapt to imperfect data, nonlinearity, and arbiter function mapping. Moreover, a neural network is better able to recognize the high level features, such as the serial correlation if any of a training set [38]. [29] showed that the ANN method was the best performing model over the Naïve 1, moving average, exponential smoothing and multiple regression even for a smallsized training set and a high level of random errors. Similar results were obtained by [5, 7, and 25]. Some drawbacks of this method is the looser linkage to theory and the inability to yield useful parameters of independent variables impact on the tourism demand [29]. A possibility for future research could be to include some dynamic qualitative exogenous variables in the neural network model (as government policy, weather conditions, etc…..) [38].
The econometric approach to forecasting is a causal approach. It identifies cause and effect relationships between tourism demand and variables that cause the flow of tourists. Determining the explanatory variables that influence the forecast variable and the appropriate mathematical expression of this relationship is the central objective. The regression analysis explicitly addresses causal relationships that are evident in the real world so it can accommodate a wide range of relationships. These include linear and non-linear associations, as well as lagged effects of explanatory variables over several periods. 2.2.1 Selection of the variables. Following the micro economic theory, there are some determinant factors of tourism demand: discretionary income, the tourism cost in the destination, the tourism cost of substitutive and complementary destinations, cost of travel, cost of travel to the substitutive and complementary destinations, exchange rates, population of the origin country, marketing expenditures, the lagged dependent variable (represent word of mouth , consumer habitual behavior), time trend variable (to account for the impacts of tourists' tastes, demographic changes in the origin countries), dummy variables (to account for oneoff- events), etc…. [10, 14, 46 and 54]. The explanatory variables included in the tourism demand vary enormously with research objectives and the availability of the data. Tourism demand can be measured using tourist numbers, tourist nights and tourism expenditure. Total tourist arrivals are the most frequently using measure of tourism demand [43, 44, 46 and 54].
2.3. Other emerging quantitative models Some recent techniques have emerged recently such artificial intelligence techniques and tourism technical analysis system. 2.3.1 The artificial intelligence techniques (AI techniques. Traditionally AI techniques derived from the rule- based and logic programming systems, while
2.3.1.2 The fuzzy time-series method. Fuzzy logic is a relatively new field of mathematics, which recognizes the vagueness of reality. Exact measurements cannot always convey the true picture of reality, because reality viewed in totality is vague, hazy and unclear. It has strengths in analyzing a short time series. It has been applied by [52] to forecast tourist arrivals to Taiwan, but forecasting performance of fuzzy time series methods needs further researches. 2.3.1.3 The rough set approach. Similar to the fuzzy logic, the rough set theory focuses on uncertain or incomplete knowledge (data) by incorporating the classic set theory [3, p.70]. The rough set approach models the relations amongst a set of mixed numeric and non-numeric variables, for example it pays much attention to the categorial variables such as demographic features and predicts tourism demand level. It has been applied in the tourism industry by [3]. 2.3.1.4 Genetic Algorithms (GAs). The GAs are adaptive heuristic search algorithms concluded from the ideas of natural selection and genetics [43]. [5, 19] demonstrated that this algorithm is suitable for explaining changes in the composition of tourism demand.
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2.3.1.5 The support vector machine (SVM). It can be used in solving the classification, non linear regression estimation and forecasting problems [43]. Empirical evidences showed that the SVM was superior to ARIMA and SARIMA models in forecasting tourism demand [38]. Future studies should be extended to incorporate explanatory variables. Moreover its forecasting performance should also be investigated. 2.3.2 Tourism technical analysis system (TTAS). It is an alternative approach for forecasting, it combines the Theta model decomposition [2] and technical analysis techniques [41]. The concept of using the TA in tourism demand forecasting arises from the fact that tourism markets behave more or less like stock markets. The method used the Theta model decomposition in order to construct two new time series, the long trend line and the short trend line. These two new time series are extrapolated separately and after equal–weighted combination, final point forecasts are produced. The TTAS produced accurate forecasts compared with Naïve 1 and 2, exponential smoothing, Gompertz, trend curve analysis, autoregression and classical econometric model [39]. In condition of direction change error and trend change error, it performs with a reasonable level of accuracy. The TTAS can overcome the problem of data availability which often limits the performance of econometric models (it can be used with short timeseries data). The major future advance for TTAS is to incorporate the ability to cope with one-off-events, this would make extremely flexibly TTAS to shocks. Moreover, future studies should investigate the forecasting performance of TTAS method compared with advanced econometric and time series models [39].
3. Econometric Modeling There are two major approaches to causal modeling in tourism demand forecasting. The first is the single equation where the forecast variable is dependent on, or explained by, other independent variables. The second is the structure econometric models. Previous literature on econometric modeling is divided into traditional models and recent models. Traditional regression models suffer from a number of problems including: 1- The structure stability of the models and a belief that the future will be similar to the past which is an unrealistic assumption [47]. The dynamic characteristics of demand behavior are ignored and this may lead to poor forecasting performance. 2- Spurious regression in which the correlations between the dependent and the independent variables are exaggerated due to the use of the
trended time series, it ignores data nonstationarity [28, 45, 54, and 58]. 3- Its extensive data mining [18], as different researchers may obtain different model specification based on the same data [45]. Therefore the traditional regression models suffer from forecasting failure. Moreover, the traditional regression models were specified with very limited diagnostic statistics being reported [43]. They have ignored unit root tests and co-integration and hence, are vulnerable to the spurious regression problem. An economic time series often display non-stationary characteristics. It is important in model determination to know how to model the non-stationarity of the data (A series that has unit roots is known as nonstationarity time series) [35 and 40]. Traditional econometric models and some recent ones have failed to differentiate data and account for error correction terms when it is I(1). The results obtained from dataseries in the absence of the unit root test cannot be constructed as long-run parameter estimates [35].
3.1 Co-integration and error correction models (ECM) Co-integration describes the existence of an equilibrium or stationary relationship among two or more time series, each of which is individually nonstationary. The advantage of the co-integration approach is that it allows integration of the long-run and short-run relationships between variables within a unified framework [35]. The presence of co-integration rules out the spurious regression problem. The ECM can adjust itself toward equilibrium (the long run co-integration relationship) [45]. Furthermore, it provide a way of combining both levels and differences of variables, hence capturing the dynamics of both short run (differenced variables) and long run ( levels of the variables) elasticities. Several recent studies have used the ECM to forecast tourism demand, for example [24, 27, and 44]. The ECM can be specified as: ΔYt = (current and lagged ΔX jts , lagged ΔYts ) k
− (1 − φ1 )[Yt −1 − ∑ β j X jt −1 ] + ε t j =1
J=1,2,……k where Y is the tourism demand, X
j
(1) is the explanatory
variables, K is the number of explanatory variables,
εt
is the error term which is assumed to be white noise k
and
[Yt −1 − ∑ β j X jt −1 ] is called the disequilibrium j =1
error [47]. The ECM has no restrictions on the coefficients [45]. The co-integration relationships between tourism
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demand and the explanatory variables have taken two routes: 1- Single equation based tests such as [12 and 53] who assume that there is only one long run co-integration relationship [47 and 58]. 2- System of equations-based tests such as the JML method [21 and 22] who can detect more than one cointegration relationship in a multivariate system [47].
3.2 The autoregressive distributed lag model (ADLM) It is a general dynamic model which encompasses a number of specific models (simple autoregressive, static growth rate, leading indicator, partial adjustment, finite distributed lag, dead start and ECM). The ADLM is: k
p
p
Yt = α + ∑ ∑ β j X jt −i + ∑ φYt −i + ε t j =1 i =1
(2)
i =1
where p is the lag length. The lag length of the time series may vary and they are normally decided by experimentation [45], with certain restrictions imposed on the parameters in eq.2, a number of specific models may be derived. The final models are selected on the basis of various restrictions tests and diagnostic statistics. If the restrictions are shown to be valid, then the specific model is preferred to the general ADLM. If all the restrictions are rejected, this means that the general model is preferred. However, if the restrictions for one or more specific models are not rejected, the best specific model for forecasting and policy purposes will have to be chosen on the basis of a number of diagnostic statistics [45]. If the structure of the specific model obtained using the reduction process is a combination of restricted models, than it is termed a mixed model. The error correction mechanism is embedded in the ADLM model, therefore the spurious regression problem can be overcome by the ADLM model [45], eq.2 can be rewritten on an ECM (eq.1). From the limitations of this approach that the structure of the selected model relies too much on the data, even though economic theory play an important role in the initial specification of the general model [45, 47 and 58). The ADLM was employed in several studies as [45 and 47].
3.3 The time varying parameter model (TVP) Previous econometric models of tourism demand forecasting assume that the structure of the model used for forecasting is constant over time, i.e the parameters of the model remain unchanged over the sample period, this assumption may be too restrictive.
The TVP approach allows for structure instability, and therefore has been successfully used in modeling and forecasting, providing accurate forecasts compared with other econometric and time series models [39, 43 and 47]. Dummy variables may be used to tackle the problem of a model structure that is unstable over time if the instability is caused by one-off type change. If the instability is caused by steady changes throughout the estimation period, this can be presented by a deterministic trend. Both are not effective if the rate of change varies over time. Dummy variables are not included in the model estimation using TVP since the approach is designed to capture the effects of shocks to the system [47]. The TVP approach allows such parameters to change over time, and so is more acceptable in dealing with structural change in econometric models [13]. Although recursive OLS is useful for examining the structure stability of the model, it does not differ from traditional OLS when all data points are used to estimate the model, and therefore structural changes cannot be accommodated in generating out-of sample forecasts. The TVP uses an updating estimation process in which the most recent information is weighted more heavily than the information obtained in the distant past. Using ADLM expressed in eq.2 and with the restriction p=o imposed on the coefficients, the TVP model may be defined as: k
Yt = α + ∑ β jt X jt + ε t
(3)
j =1
m
β jt = φ j 0 + ∑ φ jh β jt − h + W jt h =1
j=0,1,2,……..,k (4) Eq.3 is the system or measurement equation, eq.4 is the transition equation which is used to stimulate how the parameters in the system equation evolve over time. The transition equation is normally specified as an autoregressive process, the most commonly used specification of the transition equation is the random walk process [47]. (5) β jt = β jt −1 + W jt j=1,2,…..…,k Equation 3,4,5 can be estimated using the SS (state pace ) model known as the Kalman Filter Algorithm [17 and 23]. The Kalman Filter is a recursive procedure for calculating the optimal estimator to the state vector giving all the information available at time t [47]. The TVP performance shows superiority over other models for short turn forecasting, this suggest that it is important to take structure instability into consideration even for short-term forecasts [44 and 47]. [47] showed that the TVP model generates the most accurate one and two years ahead forecasts. [33] integrated the merits of TVP model and ECM to
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develop a more advanced TVP-ECM. They found the overwhelming forecasting strength of TVP-ECM over a number of econometric alternatives and time series models.
3.4 Panel data analysis The panel data analysis incorporates much richer information from both time series and cross sectional data. This analysis has been infrequent in the empirical literature of tourism demand. This kind of data set has several advantages when compared with the use of time series or cross-sectional data, such as a larger number of degrees of freedom, reduced multicolinearity, higher precision of the estimates and reduction of omitted variables bias [14]. This analysis is suitable for forecasting the tourism demand when the time series for all variables are shorter, and crosssectional information on these variables are also available. [14] estimate the coefficients of the model under the assumption that the coefficients (parameters) are the same for all the countries and that the unobservable variable (the intercept) that exist influence tourism demand and are different across countries and constant over time, i.e, they assume that visitors from the countries react in the same way to changes in different explanatory variables. There is, however a set of specific characteristics for each country (such as distance of each country, cultural level of the population, the income distribution, the time available for vacations, the age structure of the population and common language) that are responsible for the differences in the observed behavior . Few studies have used these model such as [14, 36 and42], however the forecasting ability has not yet been investigated in the tourism literature.
3.5 Structural econometric models Unlike the previous approach which is known as the single-equation modeling approach, where the explanatory variables included in the models should be exogenous. The structural econometric approach can include any number of simultaneous multiple regression equations (and) denote systems of linear equations involving several interdependent variables [34]. Structural econometric models offer a number of advantages over single equation models as they more fully represent the interdependencies of variables in the real world. The following discussion will illustrate recent econometric models which used this approach. 3.5.1 The structural equal model (SEM). SEMs are simultaneous equations models, in which variables may influence one another reciprocally [43]. Only one study [51] used SEM model. They developed a SEM to estimate the relationships between all the explanatory
variables. Their study demonstrated the potential of SEMs in widening the variety of explanatory factors working together in a complex manner. 3.5.2 Vector autoregressive model (VAR). VAR model treats all the variables as endogenous, and each variable is specified as a linear relationship of the others. All the variables apart from the deterministic variables such trends, intercept and dummy variables are modeled purely as dynamic process [43]. The current values of the variables are regressed against lagged values of all the variables in the system [46]. It is a theory based approach, therefore, it permits policy simulation via the impulse response analysis. The lagged dependent variable that reflects word of mouth effects and consumer habit persistence is automatically included in the VAR specification [46]. Another advantage of this model that it does not require the generation of forecasts for the explanatory variables before the forecasts of the dependent variable can be obtained. The VAR model can be specified as:
X t = ∏ 1 X t −1 + ∏ 2 X t − 2 + ......... + ∏ p X t − p + ε t (6)
k × t matrix of variables in the system. ∏i is a k × k matrix of parameters, ε t is a vector of
Where X t is
regression errors which are assumed to be contemporaneously correlated but not autocorrelated . Eq.6 suggests that the current values of the variables should be regressed against lagged values of all the variables in the system. It is important to include an appropriate lag length in the specification of the VAR model since too few lags will result in loss of information in forecasting while too many lags will result in over-parameterization. If all the coefficients of the current values of the explanatory variables in eq.6 are restricted to zero, each equation in the system becomes a special case of the ADLM [47]. The main limitation of the VAR model is its consumption of degrees of freedom in the model estimation. As well as, it did not perform well in forecasting compared with other recent econometric models [47], this is because it is a model which generates ex-ante forecasts [47 and 58]. Although, Some empirical studies such as [46, 47, 55, 56 and57] showed that the VAR model can generate relatively accurate medium and long term forecasts to tourism demand. [57] developed Bayesian VAR models (BVAR) in order to reduce the number of parameters that need to be estimated by introducing different restrictions (priors) to the unrestricted VAR model, They found significant improvements of forecast accuracy. However, their forecasting performance relative to other modern econometric models was not evaluated. The low ranking may suggest that the distinction between endogenous and exogenous variables in tourism demand forecasting models is fairly clear or at least allowing for the distinction not to be clear does not result in more
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accurate forecasts except perhaps in the longer term [47]. 3.5.3 The almost ideal demand system (AIDS). It is another system of equation approach, normally employed to examine tourism demand in a number of neighboring (potentially competing and complementary) destinations by a source market, and uses tourism expenditures as dependent variable [46]. The advantage of this methodology is that the demand for a given destination is acknowledged as a part of a global system enabling one to obtain both "own" and theoretically consistent "cross-price" elasticities essentially for policy discussions in a superior theoretical framework [10]. The AIDS approach is based on the consumer theory of choice and the stage budgeting process. It is assumed that a consumer (tourist), faced with different alternatives (destinations), chooses a destination(s) to maximize utility. Estimated models are in conformity with the basic postulates of consumer theory, homogeneity and symmetry. Early studies didn't test for co-integration. Recent works such as [9] tested for co-integration in their studies. Recent researches employed AIDS with particular attention has been paid to the dynamics of tourism demand system as in [10]. [8 and 31, and 32] combined ECM and TVP with the linear AIDS and provide more accurate forecasts. In addition to the demand elasticity analysis, the forecasting performance of this approach had been tested in several studies such as [31 and 32]. Some of these studies showed that the various versions of AIDS outperformed their fixed parameter counterparts in the overall evaluation of demand level forecasts. Comparison of forecasting performance between various dynamic LAIDS models and the co-integrated VAR model will be of great interest in future studies. From the disadvantages of this model that bias may be contained in the parameter estimates due to the use of a limited number of alternative destinations. Ideally, one should include all likely substitutable and complementary destinations in the system. However, this is very difficult due to the data limitations.
4. Discussion All recent studies have proved that static regression models (traditional econometric models) suffer from a number of problems including structural stability, and spurious regression, where the dynamic characteristics of demand behavior are ignored. The dynamic characteristics of tourism demand behavior are allowed in the ADLM and the spurious regression problem can also be overcome. However, the recent studies showed its poor forecasting performance compared with other recent econometric models. Moreover, the structure of the model relies too much on the data [45]. Recent developments in Bayesian econometrics [30] may help to reduce the over-reliance of the model specification
on the data by imposing priors on the structure of the model. The empirical results show that the TVP model generates accurate short-term forecasts [43 and 44]. This suggests that it is important to take structure instability into consideration when generating shortterm forecasts. The ECMs generate poor forecasting performance [28, 44 and 45]. [26] has suggested that a possible reason for the relatively poor forecasting accuracy of ECMs is that the level of differencing required to achieve stationarity is determined by hypothesis testing, and it is known that tests for unit roots often lack power. The VAR model produce relatively poor forecasts especially in the short-run forecasting, but for long-term forecasts, it is capable of producing accurate forecasts [45]. This may be because it generates ex-ante forecasts. The reason may be that the distinction between endogenous and exogenous variables in tourism demand forecasting models is fairly clear, or at least that allowing for the distinction not to be clear does not result in more accurate forecasts except perhaps in the longer term [43]. The Panel data analysis is another econometric model that have appeared recently in tourism demand studies. Although, it reduces the problem of multicolinearity and provides more degrees of freedom in the model estimation, it is rarely applied and the forecasting ability has not yet been investigated [14]. Some models such as the AIDS models have emerged recently, differently from other models, this model is based on the consumer theory of choice. It has a much stronger underpinning of economic theory. It is more powerful than other models with respect to tourism demand elasticity analysis. The AIDS models only used prices as an explanatory variable [10]. Comparison of forecasting performance between various dynamic linear AIDS models and other recent econometric models will be of great interest in the future. Unlike the econometric models, TTAS can provide forecasts using short time series overcoming the problem of data availability which often limits the performance of the econometric models. Although the forecasting performance of TTAS method compared with that of advanced econometric and time-series models have not yet been investigated [39]. The forecasts of the AI techniques outperform most of the models, either time-series models or econometric models. The main advantage is that these techniques are able to recognize the high level features of data. But the main limitation is the looser linkage to theory and the inability to yield useful parameters of independent variables [29 and 43]. Also, their performance suffers when the amount of data is small. Although various models showed some degrees of relative forecast accuracy under specific situations, no single method could outperform others in all occasions,
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no clear-cut evidence shows that any one model can consistently outperform other models in the forecasting competition. Although recent studies show that the more advanced and newer forecasting techniques tend to result in improved forecast accuracy under certain circumstances. As a result, some researchers have attempted to combine the forecasts generated from different models in order to improve the forecasting accuracy. The majority of forecasting studies suggests that forecast combination can improve forecasting accuracy, for example [1 and 58] examine whether combining tourism forecasts generated from different models can improve forecasting accuracy using three combination methods. The empirical results show that the forecasts combinations do not always outperform the best single forecasts. The study suggests that combination forecasts are almost certain to outperform the worst individual forecasts and avoid the risk of complete forecast failure. To overcome the limitations of quantitative forecasting and further improve forecast accuracy, several researchers have tried to integrate the quantitative forecasting methods with qualitative methods. They engage decision makers opinions with statistical techniques in the forecasting exercise using a quasi –Delphi process [49]. Further research in this respect is encouraged.
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5. Conclusion and future work In this study we have reviewed the major tourism prediction models, showing the methods and techniques they used, their advantages and their limitations. Recent advances and trends in Econometric modeling were discussed in details reaching a conclusion that there is no single forecasting model that can generate the most accurate forecasts in all situations. Moreover, if data of the explanatory variables can be obtained or estimated accurately, then the AI techniques will give the best results. When impacts of the explanatory variables for economic and policy issues need to be measured, econometric modeling approaches are more useful. If the explanatory variables can not be obtained, time series models offer the best results. Future work will be directed towards building a tourism prediction econometric model for the tourism industry in Egypt, involving features that address the special characteristics of this vital industry in Egypt.
6. Acknowledgement The authors wish to thank Dr. Amir Atteya for his help and efforts. This work is part of the ‘Data Mining for Improving Tourism Revenue in Egypt’ research project within the Egyptian ‘Data Mining and Computer Modeling Center of Excellence’.
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